Advances in Theoretical and Mathematical Physics

Volume 16 (2012)

Number 1

Equivariant modular categories via Dijkgraaf–Witten theory

Pages: 289 – 358

DOI: http://dx.doi.org/10.4310/ATMP.2012.v16.n1.a7

Authors

Jennifer Maier (School of Mathematics, Cardiff University, Wales, United Kingdom; Fachbereich Mathematik, Universität Hamburg, Germany)

Thomas Nikolaus (Fachbereich Mathematik, Universität Hamburg, Germany)

Christoph Schweigert (Fachbereich Mathematik, Universität Hamburg, Germany)

Abstract

Based on a weak action of a finite group $J$ on a finite group $G$, we present a geometric construction of $J$-equivariant Dijkgraaf–Witten theory as an extended topological field theory. The construction yields an explicitly accessible class of equivariant modular tensor categories. For the action of a group $J$ on a group $G$, the category is described as the representation category of a $J$-ribbon algebra that generalizes the Drinfel’d double of the finite group $G$.

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